Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

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The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

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Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.List;
import java.util.Queue;
import java.util.Stack;

public class PrCGridGame {
	public static void main(String[] args) throws NumberFormatException, IOException {
		// Init
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(System.out, true);
		
		// Read input
		String[] inp = in.readLine().split(" ");
		int N = Integer.parseInt(inp[0]),
			M = Integer.parseInt(inp[1]);
		
		int[][] g = new int[N][M];
		
		for (int i = 0; i < N; ++i) {
			inp = in.readLine().split(" ");
			for (int j = 0; j < M; ++j) {
				g[i][j] = Integer.parseInt(inp[j]);
			}
		}
		
		// Compute
		GridGame game = new GridGame(g, N, M);
		game.play();
		
		// Output
		if (game.totalSum > 0) {
			out.print("-1");
		} else {
			List<String> gameLog = game.getLog();
			out.println(gameLog.size());
			for (String entry: gameLog) {
				out.println(entry);
			}
		}
		
		// Finalize
		out.close();
		in.close();
	}
	
	public static class GridGame {
		int g[][];
		int rNum, cNum;
		int[] minRowValue;
		int[] minColValue;
		int totalSum;
		int minRowId, minColId;
		List<String> movesLog;
		
		public GridGame(int[][] g, int rows, int cols) {
			this.g = g;
			this.rNum = rows;
			this.cNum = cols;
			this.minRowValue = new int[rows];
			this.minColValue = new int[cols];
			this.movesLog = new ArrayList<String>(100000000);
			this.computeGameParams();
		}
		
		protected void computeGameParams() {
			Arrays.fill(minRowValue, Integer.MAX_VALUE);
			Arrays.fill(minColValue, Integer.MAX_VALUE);
			
			for (int i = 0; i < rNum; ++i) {
				for (int j = 0; j < cNum; ++j) {
					totalSum += this.g[i][j];
					minRowValue[i] = Math.min(minRowValue[i], this.g[i][j]);
					minColValue[j] = Math.min(minColValue[j], this.g[i][j]);
				}
			}
		}
		
		public void play() {
		    if (rNum >= cNum) {
		    	traverseCols();
		    	traverseRows();
		    } else {
		    	traverseRows();
		    	traverseCols();
		    }
		}
		
		
		protected void traverseRows() {
			for (int i = 0; i < rNum; ++i) {
		    	if (minRowValue[i] > 0) {
		    		move(MoveType.ROW, i, minRowValue[i]);
		    	}
		    }
		}

		protected void traverseCols() {
			for (int i = 0; i < cNum; ++i) {
		    	if (minColValue[i] > 0) {
		    		move(MoveType.COL, i, minColValue[i]);
		    	}
		    }
		}
		
		public void move(MoveType moveType, int ind, int diffValue) {
			if (diffValue == 0)
				return;
			
			switch (moveType) {
				case ROW:
					for (int i = 0; i < cNum; ++i) {
						g[ind][i] -= diffValue;
						minColValue[i] = Math.min(minColValue[i], g[ind][i]);
					}				
					minRowValue[ind] = 0;
					totalSum -= diffValue * cNum;
					break;
					
				case COL:
					default:
					for (int i = 0; i < rNum; ++i) {
						g[i][ind] -= diffValue;
						minRowValue[i] = Math.min(minRowValue[i], g[i][ind]);
					}
					minColValue[ind] = 0;
					totalSum -= diffValue * rNum;
			}
			
			log(moveType, ind, diffValue);
		}
		
		public void log(MoveType moveType, int ind, int diffValue) {
			for (int i = 0; i < diffValue; ++i) {
				movesLog.add(moveType == MoveType.ROW ? "row " + (ind + 1) : "col " + (ind + 1));
			}
		}
		
		public List<String> getLog() {
			return this.movesLog;
		}
	}
	
	public static enum MoveType {
		ROW,
		COL
	};
}